CN111737942A - Steady-state harmonic calculation method for three-phase three-wire system modular multilevel converter - Google Patents

Steady-state harmonic calculation method for three-phase three-wire system modular multilevel converter Download PDF

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CN111737942A
CN111737942A CN202010501979.6A CN202010501979A CN111737942A CN 111737942 A CN111737942 A CN 111737942A CN 202010501979 A CN202010501979 A CN 202010501979A CN 111737942 A CN111737942 A CN 111737942A
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phase
mmc
steady
bridge arm
current
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CN111737942B (en
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刘进军
陈星星
邓智峰
宋曙光
杜思行
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Xian Jiaotong University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels

Abstract

The invention discloses a three-phase three-wire system modular multilevel converter steady-state harmonic calculation method, which is used for obtaining an average circuit model of an MMC by neglecting high-frequency components of switching actions of a submodule of the MMC and only considering low-frequency components. According to the condition that the sum of three-phase current dynamic equation and three-phase three-wire system MMC three-phase current is 0, a neutral point voltage difference expression of an alternating current side and a direct current side is deduced, 12 time domain equations required by steady state analysis are written in a column according to kirchhoff voltage and current theorem and are expressed in a matrix form, the time domain expression is converted into a frequency domain according to a harmonic balance criterion and a generalized average method, and the steady state harmonic size of the current and voltage in the MMC is obtained through calculation and is used for controller design and system performance analysis. The invention considers the complete expression of the neutral point voltage difference of the AC-DC side, and the provided model can accurately analyze the harmonic characteristics of the MMC under the steady state condition no matter whether the circuit at the AC side is balanced or unbalanced and the parameters of a bridge arm are symmetrical or asymmetrical.

Description

Steady-state harmonic calculation method for three-phase three-wire system modular multilevel converter
Technical Field
The invention belongs to the technical field of power electronic power converters, and relates to a steady-state harmonic calculation method of a three-phase three-wire system modular multilevel converter.
Background
In 2001, Marquardt professor at the university of defense force of united states, munich, germany, proposed a novel Modular Multilevel Converter (MMC). The MMC expands the application voltage and power grade by adopting a mode of bridge arm cascading sub-modules, and compared with a traditional low-level converter, the MMC has the advantages of modularization, expandability, high reliability, high output waveform quality and the like. In recent years, the MMC has been widely applied to the fields of medium and high voltage electric energy conversion such as high voltage direct current transmission, medium voltage motor driving, reactive compensation, energy storage and the like.
Although the MMC has many advantages, the bridge arm sub-modules of the MMC are numerous, so that the MMC has complex steady-state harmonic characteristics. The steady state waveform analysis is the basis of MMC circuit design, controller design and system performance analysis. In the circuit design stage, the voltage and current level of the device is determined by the amplitude of a steady-state waveform; in the design stage of the controller, a steady-state working point is required to be obtained firstly, then small signal linearization is carried out on the working point, and the design of parameters of the controller is guided; steady state harmonic analysis can let the researcher further know the operating characteristic of MMC under different operating modes to optimize system overall design.
The MMC connecting structure mainly comprises a three-phase four-wire system and a three-phase three-wire system. In the three-phase four-wire system structure, a neutral point on a direct current side is directly connected with a neutral point on an alternating current side, and the voltage difference between the two points is 0; the three-phase three-wire system structure has the advantages that neutral points on the AC side and the DC side are not directly connected, and voltage difference exists between the two neutral points. Compared with a three-phase four-wire system structure, the three-phase three-wire system MMC is more widely applied to practical engineering. The steady-state analysis model of the existing MMC mainly has three types: the analysis object of the first type of model is a three-phase four-wire system MMC; the analysis object of the second type of analysis model is a three-phase three-wire system MMC, but the voltage difference of a neutral point on an AC/DC side is directly ignored in the analysis process; the analysis object of the third type model is a three-phase three-wire system MMC, and the voltage difference of a neutral point on the AC/DC side is considered. The existing first-class model and the existing second-class model cannot accurately reflect the internal harmonic characteristics of the three-phase three-wire system MMC, the third-class model can provide an accurate analysis method, but is only suitable for the conditions that an alternating current side is balanced and bridge arm parameters are symmetrical, and when the conditions that the alternating current side is unbalanced and the bridge arm parameters are asymmetrical occur, the existing third-class model can cause a large analysis error.
Disclosure of Invention
The invention provides a steady-state harmonic calculation method for a three-phase three-wire system modular multilevel converter, which can accurately analyze steady-state harmonic characteristics of the modular multilevel converter under all conditions of balance and unbalance of an alternating current side and symmetric and asymmetric bridge arm parameters.
The invention is realized by the following technical scheme:
the first step is as follows: and (4) ignoring high-frequency components of the switching action of the MMC sub-module, and only considering low-frequency components to obtain an average circuit model of the MMC.
The second step is that: according to the three-phase current dynamic equation and the condition that the sum of three-phase currents of the three-phase three-wire system MMC is 0, deducing the voltage difference expression of a neutral point at the AC/DC side as follows:
Figure BDA0002525148180000021
wherein u isnn′The voltage difference is the neutral point voltage difference of the AC side and the DC side; j represents a phase, j ═ a, b, c; u represents an upper bridge arm, and l represents a lower bridge arm; l is bridge arm inductance, and R is bridge arm resistance; u. ofoIs an AC side voltage, UdcIs a direct current side voltage; m is a bridge arm modulation function;
Figure BDA0002525148180000022
the sum of the capacitor voltages of the bridge arm submodules.
The third step: according to kirchhoff's theorem of voltage and current, 12 time domain equations required by steady state analysis are written in a column and expressed in a matrix form as follows:
Figure BDA0002525148180000023
wherein x*(t) and x (t) are unknowns matrices, A (t) and B (t) are coefficients matrices, and u (t) is an input matrix.
The fourth step: converting the time domain expression to a frequency domain according to a harmonic balance criterion and a generalized average method:
sX＝(A-Q)X+BU
ignoring dynamic components in the frequency domain equation, obtaining the amplitude and phase of the steady-state harmonic by solving the matrix equation:
X＝-(A-Q)-1BU
the fifth step: and calculating to obtain the steady-state harmonic magnitude of the current and voltage in the MMC, and using the steady-state harmonic magnitude to guide circuit design, controller design and system performance analysis.
The three-phase three-wire system MMC steady-state harmonic calculation method provided by the invention considers a complete expression of the neutral point voltage difference of the alternating current side and the direct current side, and the provided model can accurately analyze the harmonic characteristics of the MMC under the steady-state condition no matter whether the circuit at the alternating current side is balanced or unbalanced and the parameters of a bridge arm are symmetrical or asymmetrical.
Drawings
FIG. 1 is a three-phase three-wire system MMC topology diagram;
FIG. 2 is a detailed switching model and an average model of an MMC sub-module;
FIG. 3 is a detailed switching model and an average model of an MMC bridge arm;
FIG. 4 is a theoretical calculation and simulation result of a stable waveform of an MMC under the condition that an alternating current side is balanced and bridge arm parameters are symmetrical;
FIG. 5 shows theoretical calculation and simulation results of a stable waveform of an MMC under the conditions of unbalanced AC side and asymmetric bridge arm parameters.
Detailed Description
The present invention will now be described in further detail with reference to specific examples and figures, which are intended to be illustrative, but not limiting, of the invention.
The invention relates to a method for calculating steady-state harmonic waves of a three-phase system MMC. The adopted three-phase three-wire system MMC main circuit topology is shown in figure 1. Each phase of the converter is composed of an upper bridge arm and a lower bridge arm, each bridge arm comprises N cascaded half-bridge sub-modules, and the following two equations can be written in a column according to kirchhoff voltage theorem:
Figure BDA0002525148180000031
Figure BDA0002525148180000032
wherein u isojAnd iojAc side voltage and current (j ═ a, b, c), respectively; i.e. iujAnd iljRespectively the upper and lower bridge arm currents; ru(l)jAnd Lu(l)jRespectively a bridge arm resistor and an inductor; u. ofujAnd uljRespectively the upper and lower bridge arm voltages; u shapedcIs a direct current side voltage; u. ofnn′Is the neutral point voltage difference on the AC-DC side. The leg currents can be further represented as:
Figure BDA0002525148180000033
Figure BDA0002525148180000034
wherein icirjIs a circular flow iojIs an alternating side current. From the above equation, the dynamic equation for obtaining the output current and the circulating current can be derived as follows:
Figure BDA0002525148180000035
Figure BDA0002525148180000036
wherein Kj1To Kj6The expression of (a) is as follows:
Figure BDA0002525148180000037
detailed switching model of MMC half-bridge submodule as shown in FIG. 2, under constructionAnd in the modular process, the high-frequency component of the switching action is ignored, and an average model of the MMC half-bridge sub-module can be obtained. Wherein the output port voltage of the submodule is mxjUcxj(ii) a The current flowing through the sub-module capacitor is mxjixj；mxjFor sub-module modulation function (1 ≧ m)xj≥0，x＝u，l)；CxjIs the sub-module capacitance value, UcxjIs the capacitor voltage. Assuming that all sub-modules in the bridge arm are the same, the sub-modules have balanced and the same capacitance and voltage, and an average model of the bridge arm can be obtained from a switch model of the bridge arm circuit, as shown in fig. 3. Wherein
Figure BDA0002525148180000048
Is the sum of the capacitor voltages of all sub-modules in the bridge arm
Figure BDA0002525148180000049
The equivalent capacitance value in the average model of the bridge arm is Cxjand/N. The dynamic equation of the equivalent capacitance is:
Figure BDA0002525148180000041
the bridge arm voltage expression is:
Figure BDA0002525148180000042
for a three-phase three-wire system MMC system, the sum of the three-phase ac currents is 0, i.e.:
iag+ibg+icg＝0
adding the current dynamic equations of the three-phase alternating current side and according to the condition that the sum of the currents of the three-phase alternating current side is 0, the expression of the voltage difference of the neutral point of the alternating current side and the direct current side can be deduced as follows:
Figure BDA0002525148180000043
wherein:
Figure BDA0002525148180000044
will unn’Substituting the expression into a three-phase alternating-current side current dynamic equation, and writing a matrix expression of 12 time domain equations required by steady-state harmonic calculation in a column mode:
Figure BDA00025251481800000410
wherein:
Figure BDA0002525148180000045
Figure BDA0002525148180000046
u(t)＝[uoa，uob，uoc，Udc，Udc，Udc，0，0，0，0，0，0]T
Figure BDA0002525148180000047
the expression of each sub-matrix in the A (t) matrix is as follows:
Figure BDA0002525148180000051
Figure BDA0002525148180000052
Figure BDA0002525148180000053
Figure BDA0002525148180000054
Figure BDA0002525148180000055
Figure BDA0002525148180000056
Figure BDA0002525148180000057
Figure BDA0002525148180000058
Figure BDA0002525148180000059
A33(t)＝A34(t)＝A43(t)＝A44(t)＝O3
wherein O is3Is a third order zero matrix.
Figure BDA00025251481800000510
B (t) the expression of each sub-matrix in the matrix is as follows:
Figure BDA0002525148180000061
Figure BDA0002525148180000062
B13(t)＝B14(t)＝B23(t)＝B24(t)＝B31～34(t)＝B41～44(t)＝O3
according to the generalized average method and the harmonic balance principle, 12 time domain equations are converted into a frequency domain:
sX＝(A-Q)X+BU
X＝[X-k，...，X-1，X0，X1，...，Xk]T
U＝[U-k，...，U-1，U0，U1，...，Uk]T
Figure BDA0002525148180000063
Uk＝[Uoak，Uobk，Uock，Udck，Udck，Udck，0，0，0，0，0，0]
Q＝Q1-Q2+Q3
Q1＝diag(-kjω1I12，...，-jω1I12，O12，jω1I12，...，kjω1I12)
Figure BDA0002525148180000064
Figure BDA0002525148180000065
Figure BDA0002525148180000066
let the dynamic component in the frequency domain equation, that is, sX be 0, the solution of the steady-state harmonic can be obtained as follows:
X＝-(A-Q)-1BU
through the processing, the steady-state harmonic characteristic of the three-phase three-wire system modular multilevel converter can be accurately calculated and analyzed under any working condition. In order to verify the invention, fig. 4 and 5 show theoretical calculation and simulation results of a steady-state waveform. The simulation model is a three-phase three-wire system MMC system. Fig. 4 shows theoretical calculation and simulation results of a current on the ac side of a phase a, a circulating current, a sum of the upper bridge arm capacitance and the lower bridge arm capacitance and the sum of the lower bridge arm capacitance and the voltage under the condition of MMC ac side balance and completely symmetrical bridge arm parameters. The gray line is the simulation result, and the dotted line is the calculation result of the invention, so that the two are almost completely matched. FIG. 5 shows theoretical calculation and simulation results of the MMC alternating-current side voltage unbalance and the asymmetric bridge arm parameters. In the MMC three-phase circuit, the difference between the inductance and the capacitance of an upper bridge arm and a lower bridge arm of each phase is 5 percent respectively. As can be seen from fig. 5, in this case, the steady-state harmonic calculation result obtained by the present invention still matches the simulation result. The simulation and calculation results show that the method can accurately analyze the stable waveform of the MMC, and has high calculation and analysis precision under the conditions of balance and unbalance of an alternating current side and symmetrical and asymmetrical bridge arm parameters.

Claims (1)

1. A steady-state harmonic calculation method for a three-phase three-wire system modular multilevel converter is characterized by comprising the following steps of:
the first step is as follows: neglecting the high-frequency component of the switching action of the MMC sub-module, and only considering the low-frequency component to obtain an average circuit model of the MMC;
the second step is that: according to the three-phase current dynamic equation and the condition that the sum of three-phase currents of the three-phase three-wire system MMC is 0, deducing the voltage difference expression of a neutral point at the AC/DC side as follows:
Figure FDA0002525148170000011
wherein u isnn＇The voltage difference is the neutral point voltage difference of the AC side and the DC side; j represents a phase, j ═ a, b, c; u represents an upper bridge arm, and l represents a lower bridge arm; l is bridge arm inductance, and R is bridge arm resistance; u. ofoIs an AC side voltage, UdcIs a direct current side voltage; m is a bridge arm modulation function;
Figure FDA0002525148170000013
the sum of the capacitor voltages of the bridge arm submodules;
the third step: according to kirchhoff's theorem of voltage and current, 12 time domain equations required by steady state analysis are written in a column and expressed in a matrix form as follows:
Figure FDA0002525148170000012
wherein x*(t) and x (t) are unknowns matrices, A (t) and B (t) are coefficient matrices, u (t) is an input matrix;
the fourth step: converting the time domain expression to a frequency domain according to a harmonic balance criterion and a generalized average method:
sX＝(A-Q)X+BU
ignoring dynamic components in the frequency domain equation, obtaining the amplitude and phase of the steady-state harmonic by solving the matrix equation:
X＝-(A-Q)-1BU
the fifth step: and calculating to obtain the steady-state harmonic magnitude of the current and voltage in the MMC, and using the steady-state harmonic magnitude to guide circuit design, controller design and system performance analysis.
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Citations (3)

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Publication number Priority date Publication date Assignee Title
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CN110323745A (en) * 2019-07-29 2019-10-11 国网经济技术研究院有限公司 A kind of analytic method of modularization multi-level converter alternating current-direct current side harmonic propagation characteristic
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Patent Citations (3)

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Publication number Priority date Publication date Assignee Title
CN107171583A (en) * 2017-06-05 2017-09-15 南京工程学院 A kind of calculation of circulating current method of any level Modular multilevel converter
CN110323745A (en) * 2019-07-29 2019-10-11 国网经济技术研究院有限公司 A kind of analytic method of modularization multi-level converter alternating current-direct current side harmonic propagation characteristic
CN110598253A (en) * 2019-08-08 2019-12-20 上海交通大学 Multi-input multi-output frequency domain impedance modeling method for modular multilevel converter

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